The radius of eighth orbit of electron in h-atom will be more than that of fourth orbit by a factor of

h ν = Δ E = ( 1 n l o w 2 − 1 n h i g h 2 ) ⋅ 13.6 eV h\nu =\Delta E = \left(\dfrac h ν = Δ E = ( n l o w ​ 2 1 ​ − n h i g h ​ 2 1 ​ ) ⋅ 1 3 . 6 eV h, \nu, equals, delta, E, equals, left parenthesis, start fraction, 1, divided by, n, start subscript, l, o, w, end subscript, squared, end fraction, minus, start fraction, 1, divided by, n, start subscript, h, i, g, h, end subscript, squared, end fraction, right parenthesis, dot, 13, point, 6, start text, e, V, end text At the beginning of the 20th century, a new field of study known as quantum mechanics emerged. One of the founders of this field was Danish physicist Niels Bohr, who was interested in explaining the discrete line spectrum observed when light was emitted by different elements. Bohr was also interested in the structure of the atom, which was a topic of much debate at the time. Numerous models of the atom had been postulated based on experimental results including the discovery of the electron by J. J. Thomson and the discovery of the nucleus by Ernest Rutherford. Bohr supported the planetary model, in which electrons revolved around a positively charged nucleus like the rings around Saturn—or alternatively, the planets around the sun. By the early 1900s, scientists were aware that some phenomena occurred in a discrete, as opposed to continuous, manner. Physicists Max Planck and Albert Einstein had recently theorized that electromagnetic radiation not only behaves like a wave, but also sometimes like particles ca...

5 Relativity • Introduction • 5.1 Invariance of Physical Laws • 5.2 Relativity of Simultaneity • 5.3 Time Dilation • 5.4 Length Contraction • 5.5 The Lorentz Transformation • 5.6 Relativistic Velocity Transformation • 5.7 Doppler Effect for Light • 5.8 Relativistic Momentum • 5.9 Relativistic Energy • Learning Objectives By the end of this section, you will be able to: • Explain the difference between the absorption spectrum and the emission spectrum of radiation emitted by atoms • Describe the Rutherford gold foil experiment and the discovery of the atomic nucleus • Explain the atomic structure of hydrogen • Describe the postulates of the early quantum theory for the hydrogen atom • Summarize how Bohr’s quantum model of the hydrogen atom explains the radiation spectrum of atomic hydrogen Historically, Bohr’s model of the hydrogen atom is the very first model of atomic structure that correctly explained the radiation spectra of atomic hydrogen. The model has a special place in the history of physics because it introduced an early quantum theory, which brought about new developments in scientific thought and later culminated in the development of quantum mechanics. To understand the specifics of Bohr’s model, we must first review the nineteenth-century discoveries that prompted its formulation. When we use a prism to analyze white light coming from the sun, several dark lines in the solar spectrum are observed ( Fraunhofer lines after Joseph von Fraunhofer, who accurately m...

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[ "article:topic", "authorname:openstax", "absorption spectrum", "\u03b1\u03b1-particle", "\u03b1\u03b1-ray", "Balmer formula", "Balmer series", "\u03b2-ray", "Bohr radius of hydrogen", "Bohr\u2019s model of the hydrogen atom", "excited energy states of the H atom", "Fraunhofer lines", "\u03b3-ray", "ground state energy of the hydrogen atom", "Humphreys series", "hydrogen-like atom", "ionization energy", "ionization limit of the hydrogen atom", "Lyman series", "nuclear model of the atom", "Paschen series", "Pfund series", "postulates of Bohr\u2019s model", "Quantum Number", "Rutherford\u2019s gold foil experiment", "Rydberg constant for hydrogen", "Rydberg formula", "license:ccby", "showtoc:no", "transcluded:yes", "program:openstax", "source[1]-phys-4523" ] \( \newcommand\) • • • • • • • • • • Learning Objectives By the end of this section, you will be able to: • Explain the difference between the absorption spectrum and the emission spectrum of radiation emitted by atoms • Describe the Rutherford gold foil experiment and the discovery of the atomic nucleus • Explain the atomic structure of hydrogen • Describe the postulates of the early quantum theory for the hydrogen atom • Summarize how Bohr’s quantum model of the hydrogen atom explains the radiation spectrum of atomic hydrogen Historically, Bohr’s model of the hydrogen atom is the very first model of atomic structure that correctly explained the radiation spectra of atomic hydrogen. The model has a special place in the...